Inverse Kinematic Equations Research Articles

The optimization of global fault tolerant trajectory for redundant manipulator based on self-motion

The redundancy feature of manipulators provides the possibility for the fault tolerant trajectory planning. Aiming at the completion of the specific task, an algorithm of global fault tolerant trajectory optimization for redundant manipulator based on the self-motion is proposed in this paper. Firstly, inverse kinematics equation of single redundancy manipulator based on self-motion variable and null-space velocity array of Jacobian are analyzed. Secondly, the mathematical description of fault tolerance criteria of the configuration of manipulator is established and the fault tolerance configuration group of manipulator is obtained by using iteration traversal under the fault tolerance criteria. Then, considering the joint limits and minimum the energy consumption as the optimization target, the global fault tolerant joint trajectory is achieved. Finally, simulation for 7 degree of freedom (DOF) manipulator is performed, by which the effectiveness of the algorithm is validated.

Prediction of inverse kinematics of a 5-DOF pioneer robotic arm having 6-DOF end-effector using ANFIS

In this paper, a method for forward and inverse kinematics analysis of a 5-DOF pioneer robotic arm PArm having 6-DOF end-effector is proposed. Obtaining the trajectory and computing the required joint angles for a higher DOF robot manipulator is one of the important concerns in robot kinematics and control. The difficulties in solving the inverse kinematics equations of higher DOF robot manipulator arises due to the presence of uncertain, time varying and nonlinear nature of equations having transcendental functions. In this paper, the ability of adaptive neuro-fuzzy inference system ANFIS is used to the generated data for solving inverse kinematics problem. The proposed hybrid neuro-fuzzy system combines the learning capabilities of neural networks with fuzzy inference system for nonlinear function approximation. A single-output Sugeno-type fuzzy inference system FIS using grid partitioning has been modelled in this work. The Denavit-Hartenberg D-H representation is used to model robot links and solve the transformation matrices of each joint. The forward kinematics and inverse kinematics for a 5-DOF manipulator are analysed systemically.

Mechanical Design and Kinematics Analysis of a Hydraulically Actuated Manipulator

This paper gives a mechanism design of a six DOF hydraulically actuated manipulator firstly. Then its DH frames and link parameters are given. Next, its forward kinematic equations are derived according to homogeneous transformation method. Fourthly, the analytical solutions of its inverse kinematics are solved by given the position and posture of the end-effector simultaneously. The posture of the end-effector is given with three z-y-z Euler angles for they have obvious geometry meanings and are easy to be measured. In addition, the correctness of the inverse kinematic equations is verified in Simulink by comparing many sets of randomly produced joint variables in workspace and their corresponding inverse solutions.

A general method to determine compatible orientation workspaces for different types of 6-DOF parallel manipulators

This paper presents a general method to develop a compatible orientation workspace for a 6-DOF parallel manipulator. The workspace boundary for any type of manipulator can be determined using the proposed method, if the equations for inverse kinematics can be developed. The workspace boundary can be developed by solving the equations, but the results show that a search technique that uses the bisection method is more efficient, if the equations are 4th or higher degree polynomials. In general, a workspace can be developed in less than 5min, using a personal computer. The effect of the size of the platform, the passive joint limits, the link interactions and singularity on the shape and size of a workspace are also determined.

The Kinematics Analysis of the 3-PTT Parallel Machine Tools

This paper presents the kinematics for 3-PTT parallel machine tools, the kinematic is analytically performed, the forward and inverse position kinematic equations are explicit functions and workspace is derived and there is no singularity configuration and kinematic coupling in the whole workspace. The manipulability analytical of the parallel machine tool is investigated by the Jacobian matrix.

A Study of Calculation Method for Finger Joint Angular Displacement Based on the Finger Inverse Kinematics

A simple method for measuring and calculating the finger joint angular displacement was proposed to serve as the basis for designing dexterous hand and rehabilitation robot hand. The direct kinematics model and the inverse kinematics equation of the finger were established at the beginning of this paper. Then, the trajectory of the fingertip, from which the coordinates of the fingertip were extracted by using AutoCAD, was captured by camera. Finally, the trajectory coordinates of the fingertip were substituted into the inverse kinematics equations to solve the angular displacements of the proximal interphalangeal (PIP), distal interphalangeal (DIP) and metacarpophalangeal (MCP) joints. The calculating precision testing of the finger joint angular displacement needs to substitute the angular displacements calculated before into the direct kinematics equations of the finger to calculate the trajectory of the fingertip. Then, the average Euclidean distance between the calculated trajectory and the real trajectory was computed to test the calculating precision of the finger joint angular displacement. The average Euclidean distance of each fingers is less than 0.05mm, which proves the high calculating precision of the finger joint angular displacement and the efficiency of the method presented in this paper.

Analytical and semi-analytical inverse kinematics of SSRMS-type manipulators with single joint locked failure

Redundant space manipulators, including Space Station Remote Manipulator System (SSRMS), Special Purpose Dexterous Manipulator (SPDM) and European Robotic Arm (ERA), have been playing important roles in the construction and maintenance of International Space Station (ISS). They all have 7 revolute joints arranged in similar configurations, and are referred to as SSRMS-type manipulators.When a joint is locked in an arbitrary position due to some failures, a 7R manipulator degrades to a 6R manipulator. Without a spherical wrist or three consecutive parallel joints, the inverse kinematics of the 6R manipulator is very complex. In this paper, we propose effective methods to resolve the inverse kinematics for different cases of any joint locked in an arbitrary position. Firstly, configuration characteristics of the SSRMS-type redundant manipulators are analyzed. Then, an existing of closed-form inverse kinematics is discussed for locking different joints. Secondly, D–H frames and corresponding D–H parameters of the new 6-DOF manipulator formed by locking a joint in an arbitrary position are re-constructed. A unified table is then created to describe the kinematics for all possible cases of single joint locking failure. Thirdly, completely analytical and semi-analytical methods are presented to solve the inverse kinematics equations, and the former is used for locking joint 1, 2, 6 or 7 while the latter for locking joint 3, 4 or 5. Finally, typical cases for single joint locking are studied. The results verify the proposed methods.

Design for Several Hydraulic Parameters of a Quadruped Robot

For a quadruped robot with 12 active joints driven by linear hydraulic actuators, some important parameters, such as the oil flow of the hydraulic system and the needed maximum output force of eac h actuator, are hard to calculate precisely with kinematics and dynamics equations. The oil flow is mainly determined by the walking speed o f the quadruped robot, but also influenced by the stride frequency, gait type and the foot trajectory. This paper planned the fo ot trajectory with cubic polynomial firstly. Then selected optimal stride frequency referred to that of four-legged mammals and stride length according to the required walking speed of the quadruped robot. Furthermore, displacement curves and velocity curves with respect to time for all linear hydraulic actuators can be obtained easily with inverse kinematics equations in MATLAB. The needed maximum output force of each actuator can be obtained from dynamic simulation with MSC.ADAMS. Then the effective area of the hydraulic actuator can be calculated according to the output force of actuator and oil pressure of the hydraulic system. Lastly, the oil flow can be calculated precisely by summing all the products of the velocity and the effective area of each actuator.

Control System Design and Trajectory Planning for SCARA Robots

Based on STM32F407ZET6 microprocessor with ARM Cortex-M4 core, we designed a controller for servo motors and servo drivers of a 4-axis Selective Compliance Assembly Robot Arm (SCARA) robot. The forward and inverse kinematic equations are established, circular interpolation equations in three-dimensional space are derived by using the digital differential analyzer method. The adopted circular interpolation algorithm avoids to judge quadrant and feeding direction, which simplifies the program.

Postural analysis and workspace design using an analytically derived inverse kinematics model

A kinematics model of the upper limb was developed using three degrees of freedom on the shoulder and one on the elbow. Whilst the direct kinematics equation computes the position of the hand, the inverse kinematics equation provides the upper limb's joint angles related to a given posture. Only after defining a discomfort cost function that accounts for the joint's displacement from the neutral position, the inverse kinematics equation for this model proved analytically solvable. Such solution was used in conjunction with observational postural assessment methods in order to improve the subjective estimation of the joint angles. Besides that, it was shown the utility of the direct kinematics equation in the rearrangement of the elements of the workplace.

Trajectory Planning and Walking Pattern Generation of Humanoid Robot Motion

Walking trajectory generation for a humanoid robot is a challenging control issue. In this paper, a walking cycle has been recognized considering human motion, and nine simple steps were distinguished in a full step of walking which form motion trajectory, and generates a simplified ZMP motion formulation. This system was used in humanoid robot simulation motion and is achievable easily in walking steps of robot. A minimum DOFs humanoid robot has been considered and geometrical relationships between the robot links were presented by the Denavit-Hartenberg method. The inverse kinematics equations have been solved regarding to extracted ZMP trajectory formula, and constraints in different steps. As a result; angular velocity, acceleration and power of motors were obtained using the relationships and Jacobin. At each step, extracted data were applied on simulated robot in Matlab, and Visual Nastran software. Zero moment point trajectory was evaluated in simulation environment.

A Novel Hydraulic Spherical Joint and Motion Analysis

Proposing a new type of hydraulic drive spherical joint with two degrees of freedom.The joint mechanism has the advantages of hydraulic and also can rotate with multi-degrees of freedom. Based on the mechanism theory, the forward and inverse kinematics equations are derivated and the singular configuration and workspace of the mechanism are found. The spherical joint mechanism has these characteristics: a compact structure, low coupling, large load, and the joint can complete the omni-directional output.

Error analysis and optimization of a 3-degree of freedom translational Parallel Kinematic Machine

In this paper, error modeling and analysis of a typical 3-degree of freedom translational Parallel Kinematic Machine is presented. This mechanism provides translational motion along the Cartesian X-, Y- and Z-axes. It consists of three limbs each having an arm and forearm with prismatic-revolute-revolute-revolute joints. The moving or tool platform maintains same orientation in the entire workspace due to its joint arrangement. From inverse kinematics, the joint angles for a given position of tool platform necessary for the error modeling and analysis are obtained. Error modeling is done based on the differentiation of the inverse kinematic equations. Variation of pose errors along X, Y and Z directions for a set of dimensions of the parallel kinematic machine is presented. A non-dimensional performance index, namely, global error transformation index is used to study the influence of dimensions and its corresponding global maximum pose error is reported. An attempt is made to find the optimal dimensions of the Parallel Kinematic Machine using Genetic Algorithms in MATLAB. The methodology presented and the results obtained are useful for predicting the performance capability of the Parallel Kinematic Machine under study.

Development of Sensor and Control Systems of a Wearable Robot to Walk on a Step

SUMMARYThe goal of our study is to develop a system for walking on a step using a wearable robot. Our system consists of (1) sensing of a step from the movement of the walker, (2) detection of the foot placement state related to the step, and (3) generation of gait patterns of climbing and stepping down for the step. In the generation of gait patterns for the step, toe trajectories are generated according to the height of the step to avoid collision of the swinging leg with the step. The hip trajectory is generated by an optimization technique that minimizes the sum of the joint angular jerk of the robot subject to constraints on the hip position and the velocity at toe liftoff. Each joint angle trajectory is calculated from the generated trajectories by means of inverse kinematic equations. We investigated the feasibility of the proposed sensor and control systems for two steps with different heights.

Design and analysis of a tendon-based MRI-compatible surgery robot for transperineal prostate needle placement

Tendon-based transmission has significant advantages in the development of a surgical robot, which is fully magnetic resonance imaging compatible and can work dexterously in the very limited space inside magnetic resonance imaging core. According to the requirements of magnetic resonance imaging compatibility, a novel 6 degrees of freedom tendon-based surgical robot composed of three independent modules is developed in this paper. After a brief introduction to the robot, the direct and inverse kinematic equations are deduced by applying the concept of screw displacements, and the reachable workspace of the robot is calculated. As to the static force analysis, we apply the principle of virtual work to derive a transmission between the equivalent joint torques and the tendon forces. By the use of the pseudoinverse technique, a systematic method is developed for the resolution of redundant tendon forces.

Design and Qualification of a Parallel Robotic Platform to Assist With Beating-Heart Intracardiac Interventions

Using robotic systems to assist with sophisticated medical interventions such as aortic valve replacement under beating heart conditions necessitates the development of dexterous manipulators to ensure a safe and reliable operation. These mechanisms should not only be capable of tracking the desired trajectories with a high level of accuracy but also need to cope with strict medical constraints such as environment compatibility, patient safety and compactness. In this paper, we propose to design and experimentally qualify a robotic platform that takes into account the aforementioned requirements. Benefiting from the features of a parallel architecture, this four degrees of freedom (DOF) magnetic resonance imaging (MRI)-compatible patient-mounted and cable-driven manipulator (ROBOCATHETER) seeks to steer cardiac catheters under beating heart condition, while suitably addressing the deficiencies that currently used manipulators vastly suffer from. In addition to the detailed description of the robot design and its dedicated power transmission system, we also present the derivation of the robot's forward and inverse kinematic equations. The control algorithm implemented for the system actuation is a varying-gain proportional-integral-derivative (PID) controller, whose tracking performance will be examined.

Robust industrial robot real-time positioning system using VW-camera-space manipulation method

Purpose– Vision-based positioning without camera calibration, using uncalibrated industrial robots, is a challenging research problem. To address the issue, an uncalibrated industrial robot real-time positioning system has been developed in this paper. The paper aims to discuss these issues.Design/methodology/approach– The software and hardware of this system as well as the methodology are described. Direct and inverse kinematics equations that map joint space into “camera space” are developed. The camera-space manipulation (CSM) algorithm has been employed and improved with varying weights on camera samples of the robot end effector, and the improved CSM is named VW-CSM. The experiments of robot positioning have been conducted using the traditional CSM algorithm and the varying-weight CSM (VW-CSM) algorithm, respectively, both without separate camera calibration. The impact on the accuracy and real-time performance of the system caused by different weights has been examined and discussed.Findings– The experimental results show that the accuracy and real-time performance of the system with the VW-CSM algorithm is better than the one with using the original CSM algorithm, and the impact on the accuracy and real-time performance of the system caused by different weights has been revealed.Originality/value– The accuracy and real-time performance of the system with the VW-CSM algorithm is verified. These results prove that the developed system using the VW-CSM algorithm can satisfy the requirements of most industrial applications and can be widely used in the field of industrial robots.

Design & Kinematics Analysis of a Tracked Omnidirectional Mobile Platform

For the existing problems of wheeled omnidirectional mobile platforms in engineering applications such as big vibration and bad road adaptability, and basing on the structure of the mecanum wheel and traditional track, propose the structure of a omnidirectional mobile track, and analyse the motion principles of the track. Basing on the track, design a tracked omnidirectional mobile platform and according to the inverse kinematics equation of the platform, confirm that it can meet the essential condition for omnidirectional motion. Point out the problem of steering slip,analyse the relationship between the maximum slip ratio and its structural parameters, and propose the design criteria for it;Basing on its virtual prototype, accomplish simulation tests of transverse, diagonal and centre-steering motion. According to simulation results, it is verified that the platform can implement omnidirectional motion, meanwhile the correctness of the inverse kinematics equation of the platform is verified, consequently the theoretical basis for motion control of the platform is established.

Motion Control of a Robot Arm

The article designs a seven joints robot arm using PC-based controller. The system architecture of the robot arm contains seven DC servomotors, seven driver devices and a NI motion control card. The robot arm uses proximity sensors to locate the limit position, and programs motion trajectories to finish assigned tasks. We tune the parameters of the PID controller for the robot arm, and get the nice response to control the robot arm moving to the assigned position. The user interface is developed to control each DC servomotor using Visual Basic. The paper computes the kinematic equations of the seven joints robot arm, and calculates the motion displacement of each joint using inverse kinematic equation. The controller of the robot arm can implement precision point to point motion trajectories, and programs the motion paths on the user interface. In the experimental result, users can program the word type in the user interface. The robot arm catches the pin to write the word in the plane.

A kinematic calibration method of a 3-DOF secondary mirror of the giant magellan telescope based on least square algorithm

Because of manufacturing and assembly errors in the geometric parameters of parallel robots, calibrating the parameters is necessary for improving the positioning accuracy. The objective of this study is a 3-DOF secondary mirror of the giant Magellan telescope, which is operated by a 3-DOF parallel robot. In this paper, a kinematic calibration method is presented. In this method, a moving platform is commanded to execute a sinusoidal movement by the cooperation of three piezoelectric actuators, and experimental data is obtained using capacitive sensors. The inverse kinematic and forward kinematic equations for the local system are illustrated in this paper. Furthermore, importantly, a least square algorithm is implemented to reduce the residual between the experimental values and expected values. Additionally, a simulation model is developed for supervising the movement of the system. Results of experiment show that the method used in this paper is effective and efficient.